It's difficult to say because different users will have quite different requirements.
Some people love Picasa or Digikam. I like to just use something like Xnview . In the past some of these programs would have been difficult to install in Puppy, but hopefully that will no longer be the case with the new Puppies based on Ubuntu etc.
You should probably look at Shotwell as well.
RawTherapee or Lightzone (I don't know if you can still get the free older Linux version from anywhere) might be helpful.
I think a couple of other programs that are specifically for photo management posted here a while ago, but I can't remember what they were called _________________DEATH TO SPREADSHEETS
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Classic Puppy quotes
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Beware the demented serfers!